Scaling data using cohens d

I have 2 data sets. Data1, Data2. Data1 has a cohens d effect size of approximately 0.5141. How can I scale Data2 using this effect size? Any help would be great, I am very novice at coding. Thank you.

[dpb]

Scaling for what purpose and why?

All Cohen's d is telling you is that the difference in means between the two datasets is approximately 1/2 the average standard deviation of the two. That implies that something like 70% of the observations in set 2 would be less than the average of set 1 which is a marginally sizable difference in average relative to the variance of the data.

Without some other rationale for making any scaling differences in either set, there would seem no justification to do anything with either set.

Have to provide far more background than we have so far...

[Jorge Young]

I appreciate the response and I understand it is very vague. Cohens d in this instance is the effect some variable had on data set 1. If that same variable was introduced to data set 2 the assumption is that the shift would be the same. I do not know how to shift the distribution of data set 2 to the same effect as data set 1. hopefully this is enough background. thanks.

[dpb]

Without a lot more information to go on, I'd say just add the difference in means if the assumption is the effect is the same.

Answer 1

[Ishaan]

Hey @Jorge Young,

I notice that you intend to scale the 2nd dataset in a way that a variable has the same effect on it as the 1st dataset.

To achieve this, you need to translate that standardized difference into a raw shift in 2nd dataset’s values. There are 2 ways you can go about it.

NOTE: These strategies assume that the conditions for underlying the use of Cohen's d are met, such as normality and homogeneity of variances, especially when applying these methods to real-world data.

1. Using 2nd dataset’s own standard deviation

s2 = std(Data2); % Compute standard deviation of Data2
delta = cohens_d * s2; % Compute the shift
Data2_shifted = Data2 + delta; % Shift Data2

This will shift the 2nd dataset by Cohen’s D times the original standard deviation. Hence making the standardized shift relative to the original spread equal to the Cohen’s d value.

Use this method if you believe the intervention has the same relative strength (i.e. same standardized effect) in each dataset.

2. Using the absolute shift observed in 1st dataset.

If you have access to the absolute shift observed in the 1stdataset, then you can just add that to the 2nd dataset. This approach treats the intervention as having the same number of “units” of change irrespective of the measurement you’re using. For clarity, the absolute shift is the same as the Cohen’s d times the pooled standard deviation.

Use this method if both datasets have identical measurement scales and variances.

Here is a sample code snippet for both the options.

% Example data
rng(0); % For reproducibility
Data1_control = 50 + 10 * randn(100,1);
Data1_treatment = 55 + 10 * randn(100,1);
Data2 = 30 + 5 * randn(100,1);

% Compute Cohen's d for the 1st dataset
s1_control = std(Data1_control,0);
s1_treatment = std(Data1_treatment,0);
n1 = numel(Data1_control);
n2 = numel(Data1_treatment);
pooled_sd = sqrt(((n1-1)*s1_control^2 + (n2-1)*s1_treatment^2)/(n1+n2-2));
cohens_d_est = (mean(Data1_treatment) - mean(Data1_control)) / pooled_sd; % 0.5141

% Option 1: Scale based on 2nd dataset’s own spread
s2 = std(Data2, 0);
delta1 = cohens_d_est * s2;
Data2_shifted1 = Data2 + delta1;

% Option 2: Scale based on raw effect from the 1stdataset
delta2 = cohens_d_est * pooled_sd;
Data2_shifted2 = Data2 + delta2;

Hope this helped!